This is a guest post by Prof. Jim Schombert

Greetings Stacy’s blog readers! My name is Jim Schombert, I’ve been working with Stacy for about a quarter of a Hubble time. I knew him when his hair was brown.

In any case, I asked him if I could make a contribution to the dark matter discussion. Partly this is motivated by the LUX-ZEPLIN ‘detection’, but also cause there are some clear red flags from a philosophy of science viewpoint. I was a philosophy major in college, switched to astronomy when I 1) realized there was no money in philosophy, and 2) people at parties would talk to an astronomy major, not so much a philosophy major. I never lost my interest in the philosophy of science, tried to keep up with the literature, so how should we view the current MOND vs dark matter debate from a philosophical view? (and for a more sophisticated analysis of the topics below, I direct the reader to Merritt’s superb books and articles on MOND).

There are basically two types of philosophers when it comes to science, one type is heavy in mathematical logic and deep discussions of foundations of science, the other type is more concerned about how science is done, i.e. the history and impact side of science. All of us know the key writers of this second type of philosophy of science; Popper, Kuhn, Lakatos (hereafter PKL). You will know them cause when you read their works you will immediately recognize yourself and colleagues in their descriptions. You basically have this strong sense that we operate on our data and computer simulations just as described by these famous thinkers. In short form, Popper = ‘falsification’, Kuhn = ‘paradigms’, Lakatos = ‘research programs’, we will expand upon this below.

We all know there is no ‘truth’ to our science, you can never prove a scientific idea, you can only test it, hard, in an attempt to falsify it (Popper). The more the idea stands up to testing, the ‘stronger’ it gets, where stronger means more used/accepted by the community. Paradigms (Kuhn) are now thought of more as frameworks (think Newtonian mechanics), and research programs (Lakatos) are like giant factories of ideas that define how we come up with new ideas to test. Key to all this was that PKL insisted that this only worked when discussing the history of science, and the philosophy community was deeply disappointed in the works of PKL because they wanted criteria that could be applied in the moment (i.e., some system to assist the science community in directing science to more productive methods and goals). It’s obvious to all of us (who have been doing science for awhile) that this description is more of an idealization and usually doesn’t work (pick any observing or funding review panel as an example of how this just fails in the moment, but works well in retrospect).

Let’s take a very simple example (that almost everyone is familiar with) to see how the methods proposed by PKL work best in hindsight and are fairly useless in the moment. Consider Newtonian gravity in the mid-19th century (by the way, did you know that Ptolemy’s system of epicycles was used by the makers of almanacs into the 20th century? The math was simpler and just as accurate as using Newton. But I digress). So, a wobble in the orbit of Uranus. Abandon Newton? Hell no, the framework/paradigm has solved so many problems. Consider an auxiliary hypothesis, i.e. another planet. Right there, Neptune! Boy, how strong is your paradigm that predicts new planets. Better telescopes, more accurate data, hmm, wobble in Mercury. Obviously, try the same hypothesis (the so-called planet of Vulcan). Nothing found, fortunately relativity came along pretty soon (although it’s goal was not to solve Mercury’s orbit, it had bigger issues to address). Newtonian physics survives, but now with limits on its applications (stick to low energies). In the moment, it was hard to see the depth of the problem or the need for radical change.

In any case, us working astronomers immediately recognize this kind of scientific effort; the nuts-and-bolts, thinking about new ideas, new technology, new data – in our own research. Now let’s turn to the dark matter paradigm. For the readers of this blog, I don’t need to discuss the details of the LCDM paradigm. In brief, Oort discrepancy (1960’s), flat rotation curves (1970’s), cluster M/L’s (1980’s), large scale structure (1990’s) and, of course, the capstone CMB+BBN+Omega_Lambda (2000’s). Historically, its important to remember that a great deal of work in the 1980’s eliminated anything made of baryons for CDM (low mass stars, black holes, planets, rocks, etc). In fact, most of us stopped even trying to explain CDM by the launch of HST, there were more interesting problems to address. We just took CDM as a black box solution; those interacting galaxy simulations looked amazing.

In the end, CDM was expected to be a gravitationally interacting, not short-lived, not hot, non-baryonic particle. With the closure of the SSC in 1992, a large number of particle physicists were suddenly out of jobs, dark matter looked like the clearest path to reach new physics (and a paycheck). And astronomers were just as guilty, Fig. 1 is a old plot from an Oemler workshop paper showing the state of the art in 1985. Notice the implication that dark matter could close the Universe (i.e., Omega = 1 all in mass; there was no Lambda back then). And a closed Universe was, for some reason*, a massive desire for the astro theoretical community. And we see the beginnings of how cosmological issues override galaxy issues for the community (there’s a nobility to doing cosmology, galaxies are dirty).

There is also no need to re-iterate the failure of the high energy community to find any dark matter particles. The amount of money and people in CDM makes the Manhattan project look like a garage shop effort (only CDM did not deliver a new weapon by the 2020’s). During this time, a few of us noticed that the baryons in galaxies were strongly tied to the ‘dark matter’. We were told that low mass dwarf galaxies were dark matter dominated, but a few of us mentioned that they are also strongly gas dominated, i.e. how did the dark matter know to dominate in galaxies with the highest gas fractions? These kinds of anomalies began to build up for observers, didn’t really appear in the theory papers.

Now let’s consider how PKL would interpret the current status of the dark matter paradigm. The emphasis by all three philosophers was to examine the historical record. This frustrates mainstream philosophers who would, ideally, like apply some criteria to the current state of affairs rather than only look at hindsight. But there may be enough historical record to, at least, determine the current trajectory for the dark matter paradigm.

Perhaps the first ‘crisis’ to the LCDM paradigm would be the discovery of the baryonic Tully-Fisher relation. The luminosity Tully-Fisher, which was only a measure of the stellar mass by way of stellar luminosity, was not very surprising to the astro/physics community for a larger galaxy would have more stars and dark matter, thus higher rotation velocities. The mass discrepancy was obvious, vindicating the need for some sort of invisible dark matter, but the scatter was large and the relationship was distinctly non-linear at the low mass end. However, the TF relation was well mapped at the high mass end (early-type cluster galaxies) and was extremely useful at locking down cluster distances and mapping large scale structure.

It was Stacy’s superb observer’s insight to think about adding the gas mass to the stellar mass producing a total baryon mass to compare to the rotational velocity (I helped a little, the so-called BTFR). I say ‘observer insight’ for its one of those things that if you work at optical and radio telescopes you are comfortable thinking in terms of different kinds of data, and at ease turning luminosities into stellar masses (i.e., M/L) and HI fluxes into gas masses (lots of details, but that’s what data reduction and analysis is all about). The scatter was greatly reduced and the relationship was increasingly close to a linear fit in log-log space. Regardless
of your MOND vs dark matter bias, the BTFR quite simply says the total baryon mass is related to the total dark matter mass, which would make sense if you scoped a piece of the early Universe (equal proportions of baryons and dark matter) and made a galaxy.

But that’s not how galaxy formation was suppose to work (you don’t scope a piece of the Universe, those CDM halos form first, baryons fall in later), and this baryon-dark matter relationship varied in a surprising coherent fashion across Hubble types. Stacy being a deep reader of obtuse literature in the 80’s taught us that this type of behavior was exactly predicted by basic MOND, especially for the galaxies in my new LSB catalog (to which I remember responding “You’re using my galaxies to disprove Newton? Only death can save you from my wrath”). While MOND was designed to explain flat rotation curves, its key underlying premise is that there is no dark matter, baryons decide how things move, which is what the BTFR said.

Now, in a strictly Popperian methodology, is the BTFR sufficient to falsify the dark matter paradigm? No, of course not, as Kuhn points out, a paradigm that has been so successful in making predictions, and offering research paths, is not simply dropped, that would be intellectually short-sighted. There a lots of historical examples in science to support the continued investigation into dark matter after the discovery of the BTFR. In the field of electromagnetism, one does not actually observe the magnetic fields, we observe its effects and build tools to explore its behavior and derive out rules, theories and models. There is nothing unbalanced about studying invisible dark matter.

In a Popperian fashion, we continued to ‘ruthlessly test’ the BTFR with better samples, improved stellar population models, improved distances. The BTFR survived all this examination, although it risked refutation at every point (for example, many claims that it deviated from a linear power-law fit at the low and high mass ends). The current version by Duey et al. (2026) is by far one of the tightest corrections in astronomy, especially considering all the possible underlying astrophysical processes (e.g., feedback) that could easily distort any kinematic relation. And, as often stated, the slope is 4 and MOND predicted 4, before we looked.

By the time of the BTFR discovery, the CDM community was deep into normal science mode. As Kuhn would state, lots of problem-solving, training students, textbooks and workshops to give. However, MOND was having its breakthroughs. The second crisis will occur with the SPARC sample where Federico Lelli showed that not only does the total baryon mass determine the total dynamical mass (BTFR), but also on the local scale within a galaxy, the baryon density is also correlated with the kinematics point by point within a galaxy’s gravitational potential. This will become the awkwardly phrased radial acceleration relation (RAR).

The smooth change, in acceleration space, displayed by the RAR is well predicted by MOND, but is difficult to explain/reproduce in LCDM without feedback from star formation processes. And the process of adding ‘feedback’ to CDM simulations begins to feel a lot like adding epicycles to ‘save the phenomenon’. Kuhn would say that we need a shift to a new disciplinary matrix, which asks new questions, and will recognize the competence of these new baryon-to-dark matter connection. But to threaten the paradigm, anomalies like RAR and BTFR must persist across different methods, resist easy explanation, and be critical to central themes. Which they seem to do, for many observers, not so much in the theory community.

Theorists, understandably, resist the MOND framework for 1) must explain more, 2) make more precise predictions, 3) coordinate research and 4) open new avenues. These criteria were not met. Also, switching to Milgromian physics will require a complete re-training of techniques, tools and students. A huge investment in time and effort that does not immediately appeal to the theory community given the success of decades of galaxy simulations.

To most of the community, the discovery of the BTFR and RAR do not ‘feel’ like a Kuhnian science revolution seen in the historical record (e.g. Galileo discovering the phases of Venus). A better explanation of the state of current affairs is to adopt the ideas of Lakatos. The heart of Lakato’s philosophy is the role of research programs. A research program is a more expansive view of Kuhn’s paradigms that includes much of the day-to-day operation of science; teaching, grants, textbooks, workshops, presentations. For Lakatos, it was all about whether a research area was progressive or degenerate (possibly even in a zombie stage). To be progressive, for Lakatos, the dark matter framework must be predictive, successful, expanding, yet CDM appears to be in ‘zombie’ stage, ceasing to generate novel predictions, responding to failure with ad hoc adjustments, and no clear path to increase its value as a line of thinking.

MOND work seems more progressive, clean explanations for new discoveries. But it also is struggling, the path forward is not obvious. The accelerated galaxy formation model is the most interesting discovery, and maps into our newest technology, JWST. However, it has been extremely difficult to acquire funding or observing time to address MOND ideas. It’s surprising how conservative funding and telescope panels have become (let’s do one more H_o project). The risk/reward dynamic is clearly in MOND’s favor, but not until more MOND worker are appointed to review panels. I know what I’m talking about, I ran NASA ADP review for two years. So many smart people in one room, overwhelmed by the work, reduced to the easiest path of proposal ranking.

I predict the near future will be one of continued stagnation of CDM research, no progress with many excuses. Some of the excuses looking like new physics, some perhaps even getting the fever that string theory had. The ‘successes’ for CDM have all been indirect (my observations are completely explained by X type of CDM, rather than here are my observations of X type of CDM). And there is still a role for CDM to play in astronomy. Since MOND has a non-linear Poisson equation, it does not lend itself to N-body simulations with ease. And N-body work using CDM has been extremely successful in our understanding of tidal features in interacting galaxies and shell galaxies. It just has to be remembered that when one uses CDM in your simulation, you are basically allowing a proxy for different gravity, and you call it CDM. Kinda of like the softening parameters using early N-body to avoid the wacky math singularities as ‘particles’ in your galaxy simulation got too close.

*Inflation. It was Inflationary cosmology that insisted on Ωm = 1, and theorists chugged that Kool-Aid hard – Stacy

Stacy McGaugh is an astrophysicist and cosmologist who studies galaxies, dark matter, and theories of modified gravity. He is an expert on low surface brightness galaxies, a class of objects in which the stars are spread thin compared to bright galaxies like our own Milky Way. He demonstrated that these dim galaxies appear to be dark matter dominated, providing unique tests of theories of galaxy formation and modified gravity. Professor McGaugh is currently the chair of the Department of Astronomy at Case Western Reserve University in Cleveland, Ohio, and director of the Warner and Swasey Observatory. Previously he was a member of the faculty at the University of Maryland, having also held research fellowships at Rutgers, the Department of Terrestrial Magnetism of the Carnegie Institution of Washington, and the Institute of Astronomy at the University of Cambridge after earning his Ph.D. from the University of Michigan.

36 thoughts on “CDM, what would Popper do?”

  1. LCDM… ‘a paradigm that has been so successful in making predictions’.
    Remind me, would you, what those predictions were?

    2. This is a point that gets easily confused. Rather than parse here what is and is not a prediction of LCDM, I think the way I would phrase it is in terms of explanatory power. Dark matter has a lot of that, and that’s what people are reluctant to give up.
      Of course, one concern is that it may have too much explanatory power. https://youtu.be/nAruBWa7LGk?t=72

  3. nice post. As I have remarked in this forum before, my relative outsider perception is that both the CDM and MOND camps are getting more entrenched in their own “paradigms/programs”, and adding their own epicycles to address shortcomings – e.g. LCDM invokes “feedback” as a cure-all, yet cannot predict named galaxy empirical regularities. MOND variants (e.g. QUMOND, AQUAL) struggle with vertical tests while excelling radially. Clusters are a problem for both, perhaps more severe for MOND. It may prove to be helpful to relax some long-held sacred cow constraints and jointly re-attack the core issues such as:
    i) really attack the disk-halo conspiracy anew – explore possible couplings between DM and baryons – even relax cosmological constraints as needed. there is no real basis for large scale structure and cosmology to trump sub-grid physics – galaxy dynamics despite being messy have remarkable scale-free regularities – the CDM side must pay attention
    ii) explore the a_0/ H_0 “coincidence”. To quote that famous sage Kung Fu Panda – “there are no accidents” – perhaps H_0 should be re-interpreted as a gravitational metric instead of an expansion metric, it can be (and has) recovered from atomic physics.
    iii) the exact slope 4 can arise naturally from a stratified distribution of a family of DM particles – not just one single particle type.
    iv) the neutral/ionized partition of visible matter is very instructive – the larger the fraction of M_b that is neutral HI, the closer a galaxy is to the slope 4 line – the conspiracy could be a neutral/ionized partition factor with neutral HI being a very good predictor of total neutral mass
    While there is prior art on all of these – it feels like a very productive path forward is to find a way for particulate DM to recover the PREDICTIVE power of MOND, not continue to follow accommodative, post-hoc fits.

      1. indeed you have, to your eternal credit. Big fan. I do notice from your famous “tree” of DM possibilities, the implicit assumptions implicitly held sacred still are – i) the BBN interpretation of light element abundances is correct, ii) the redshift-distance relationship is compelling evidence for an expanding universe, whose expansion is accelerating, iii) H_0 is an expansion metric that must be measured, it cannot be derived, iv) DM must be non-baryonic and only interact gravitationally with baryonic matter. I am skeptical meaningful progress will be made by the joint MOND/LCDM community until one or more of the above assumptions are relaxed. Yes – they imply very different cosmologies, and can induce eye-rolls (been there, done that), but nearly four decades of futility are perhaps sendign us a message

  4. If spatially resolved baryonic information alone were sufficient to predict not only the radial dynamics but also where non-axisymmetric dynamical structure appears, how would that be interpreted within ΛCDM?

    Is that level of predictability expected from the gravitational response between baryons and the halo or would it impose an additional constraint on the dark matter distribution?

      1. Could you help me here? ‘The circular velocity attributable to the dark matter can be expressed as a simple equation which depends only on the observed distribution of baryonic mass.’
        To me the high degree of correlation between baryonic mass and rotation velocity suggests that if, there is also a DM component, it ought to constitute the same proportion of total mass in every galaxy. But my understanding is that the mass deficit varies substantially from galaxy to galaxy. Am I wrong in that understanding?

        1. You are correct that the mass deficit varies substantially.
          One would reasonably expect DM to be the same proportion of mass in every galaxy, and this was indeed the bedrock assumption for a long time, until data forced us to abandon it.

          1. Thanks. Popper argued that science progresses by making conjectures and subjecting them to refutation. To put it another way, a hypothesis makes predictions and one tests the hypothesis by its predictions. If it fails many times, it ought to be abandoned. In this case, the prediction fails but the hypothesis remains – a point you have made in other respects often enough yourself. Personally, I think Popper remains relevant and should be required reading.

  5. I consider the ‘nobility’ of letting cosmology prevail over galactic dynamics as being fake. Cosmology is easy, it’s like treating one slightly more complicated galaxy and more precisely than with galaxies. The bulk of the data, however, is clearly on the side of galaxies.

  6. I started off believing in Popper’s philosophy too, but as I got older (and more experienced in experimental physics) became dissatisfied even with Lakatos’ improvements. Nowadays I tend to lean more towards Feyerabend and “anything goes”, or as the Stanford Encyclopedia of Philosophy puts it “all methodological rules have only a limited validity”. It is not just Mercury where Newtonian physics had problems; the discovery of Pluto was expected to solve the remaining dynamical discrepancies in the orbits of Uranus and Neptune, but it proved to be far too small for this and now we know it as the first of the trans-Neptunian Objects (TNOs).

  7. Yesterday I watched a video “Are Warp Drives Actually Possible?” by Paul M. Sutter on the current scientific plausibility of warp drives. About 12 minutes into the video he brings up the dreaded (to sci-fi enthusiasts) three energy conditions imposed by the Universe. The first is the Strong Energy Condition – matter must always gravitate towards matter. The second is the Dominant Energy Condition – energy must never flow faster than light. The third is the Weak Energy Condition – local energy density must never be negative. He does concede that none of these are ironclad. Though he doesn’t mention it the last one leads to pathologies like closed time-like curves (CTC’s), which are like uber-forbidden in GR.

    That last energy condition probably rules out negative energy in any form for warp drives, or to explain the accelerated expansion of space via Dark Energy which is considered a form of positive energy. The first energy condition would appear to condemn our technological civilization to application of Newton’s action-reaction principle to achieve physical motion and defy the Earth’s or any celestial body’s gravitational pull. But, evidently, not everyone got the memo. It seems like astronomers and scientists from someplace else heeded their philosophers and wasted little time on imaginary particulate Dark Matter theories. In 2004 US Naval aviators, using multiple sensors, observed an object hovering above the Pacific Ocean and undergo fantastic accelerations. No evidence of propellers or rocket exhaust was seen. Personally, I take these instrument augmented reports to be as legitimate as the spectrum from an ore sample heated in a Bunsen burner. But, of course, everyone is entitled to their opinion.

  8. “While MOND was designed to explain flat rotation curves, its key underlying premise is that there is no dark matter, baryons decide how things move …”
    According to the empirical evidence, Milgrom is the Kepler of contemporary cosmology. It seems that Guendelman’s new version of string theory provides a mathematical basis for understanding Milgrom’s conjectured FUNDAMOND, as well as the dark energy phenomenon. The basic idea is that there are 2 new forms of spontaneous symmetry breaking (SSB) in string vibrations. The –1/2 and the Λ in Einstein’s field equations represent symmetries for the geometric tensor & the energy-momentum tensor. The 2 new forms of SSB suggest that Einstein’s field equations need slight corrections.
    Is Guendelman in the same ballpark as Newton & Einstein?
    Guendelman, E. I. “Dynamical string tension theories with target space scale invariance SSB and restoration.” The European Physical Journal C 85, no. 3 (2025): 276.
    https://link.springer.com/article/10.1140/epjc/s10052-025-13966-9
    https://arxiv.org/abs/2104.08875
    In the standard form of Einstein’s field equations,
    replace the –1/2 by–1/2 + FUNDAMOND-data-function &
    replace the Λ by Λ + dark-energy-data-function.

  9. Thank you for a thought provoking article, which also helps with understanding how different groups think, and define things. I have a philosophy related question, about two points in the article – the way DM is found to be tied to the baryonic matter, and a point you made about how you can never prove a scientific idea, only keep testing it.

    This is obviously true, there’s no proof of anything, unless one sets very specific limiting conditions, within which ideas can be shown to apply. But there are various things approaching it: near-proofs, smoking guns, strong evidence, and so on.

    As a philosopher, can you tell me what animal this is? It might be a kind of detection of DM, but a mathematical one. Or perhaps a near-proof, or something of that kind. It shows why DM is tied to the baryons, by showing that masses emit a refractive medium (RM) at a very small scale, which dissipates in the radial direction, making a graded RM.

    But it doesn’t even ‘prove’, or show, as much as that. All it shows is that masses are surrounded by a graded RM, as Eddington thought when he came up with his RM interpretation for GR.

    There’s a thing about a light beam in a graded RM – all points on the path are connected to all other points on it, via the law of refraction. You can pick two random points any distance apart, put four numbers into a version of Snell’s law, and the sides of the equation will always agree.

    I’ve shown that orbits do the same, and published it in 2023. You can pick two points on any orbit at all, perhaps just the path of a falling object, and find them to be linked by the law of refraction. The equation for that, the sides of which always agree to 16 decimal places, came from assuming matter is a rotating disturbance in the small-scale structure of space, which is like light, and can be refracted on helical paths. It’s briefly summarised here
    https://tritonstation.com/2024/06/18/rotation-curves-still-flat-after-a-million-light-years/#comment-22413

    Please tell me what animal it is! Thank you. It also has bearing on a third point in your article – the need for a new disciplinary matrix that Kuhn talked about, or a simplifying conceptual framework.

  10. All cosmologists need to be philosophically aware. A lot of cosmology is philosophy dressed up as science. Most fundamentally, it assumes a natural origin of the universe and excludes a supernatural one. Put another way, ‘matter and energy is all there is’, the beings that try to make sense of it – scientists and philosophers – are also merely matter and energy, and metaphysical concepts – e.g. truth, falsehood, morality – and experiences – e.g. joy, wonder – are generated by physical processes that exclude freedom of thought, responsibility, meaning because, ultimately, as a matter of philosophical belief, they are determined solely by physics.

    As part of this naturalism, cosmology starts with axioms (the Cosmology Principle, the Copernican Principle, hierarchical merging etc) and then strains every sinew to prove them, even when they appear to be contradicted.

    In science, one of the most fundamental principles is ‘pluralitas non est ponenda sine necessitate’, Occam’s Razor. One of the consequences of assuming that the universe has a natural origin is that it must postulate that the cosmic egg contained around 18 fundamental particles, not counting dark energy, whatever the energy of the vacuum is (if different), gravity and the dark matter particle. That’s an awful lot of plurality when you think about it.

    That anything exists is a philosophically challenging mystery. That 18 fundamentally different particles should co-exist, all with properties, and all be capable of interacting to make up the world we know, and that there should be none that are not integrated into the network of interactions that make the world possible (putative DM excepted) is surely an infinitely greater mystery.

    Why does the charge of the proton balance that of the electron? Why is the number of electrons (so far as we can tell) the same as the number of protons, making the universe electrically neutral? Why did not an equal quantity of antimatter generated in the Big Bang annihilate matter? How is it plausible that, with respect to each of the fundamental particles, the cosmic egg contained quadrillions of identical such particles? What caused the Big Bang?!

  11. Popper famously argued that the Darwinian theory of evolution was not a testable scientific theory, only a metaphysical research programme which, although not testable, could be rationally justified, criticised and corrected. In his view the same would apply to modern cosmology – it’s a metaphysical research programme.

    1. There is an important distinction between evolution (the process of DNA changing over the generations) and the theory of evolution (abiogenesis, common descent). The TOE is worldview IMO, but evolution as a process is science

  12. Stacy

    what do you think of

    The Rotation Curve of the Milky Way: State of the Art, the Keplerian Decline Debate, and Implications for Dark Matter
    Alessandro Melchiorri, Ruchika

    1. I don’t think it changes anything about what I’ve said here before. We know the MW is consistent with the RAR out to 17 kpc; what happens beyond that depends on who you ask.

  13. Thanks for the nice post, I needed my Mond ‘fix’. So unrelated, Sabine featured a paper about the milkyway rotation curves. Here https://arxiv.org/pdf/2608.10189 Figure 3 is the money shot. This is all from the Gaia data and I seem to recall some discussion of the gaia data (in the wide binaries discussion) that it had some change or something that happened between 15 and 20 kpc. This is right where the new paper finds something ‘off’. and I wonder if someone recalls that discussion. Thx

    1. With regards to Fig. 12 of this paper, which appears to show the MW off the RAR, it uses a crude baryonic mass model and does not seem to be aware of the model that fits well up to R = 17 kpc – https://iopscience.iop.org/article/10.3847/0004-637X/816/1/42 Beyond that I think that, if anything, the MW data fall on the other side of the RAR than what they depict. Indeed, their red triangles are from Jiao which is the same as the orange points that fall too fast in the blog posts cited above. So something goofy is afoot.

  14. In the transition to the MOND regime where we are, at 1.8 a0, is the MW rotation curve known well enough to distinguish between different interpolation functions? I read that the simple IF and your RAR IF do better than the standard IF. The one from PSG came out of my way of expressing MOND, g/gN = r/rM, which led to mu(x) = ([(1 + 4x^2)^1/2] – 1) / 2x

    It’s not a well known one, I later searched for it in the literature, and found it in a review paper of yours, with various different IFs, MOND: Observational
    Phenomenology and Relativistic Extensions. Do you know how it does with the MW rotation curve? It lands between the simple and standard IFs.

    1. The standard IF was favored back when we were using optical data to build mass models. Near-IR data appear to favor the simple IF, as does the Milky Way. However, the best IF is degenerate at some level with the stellar mass-to-light ratio, so it is probably OK to have something intermediate between standard and simple.

  15. I’m not sure about Popper, but Lakatos would likely find that ‘CDM’ is degenerating. This observation would also apply to ‘ΛCDM’; it fits a wide range of observations, but fitting data and *extrapolating* the fit doesn’t really qualify as making successful predictions.

    Lakatos would also note that endlessy studying different ‘solutions to the Einstein equations’ has not produced a progressive research programme. Furthermore, ‘modified gravity’ programmes suffer the same problem as ΛCDM: their predictive power arises from the *extrapolation* of a fitted function, not from a fundamental law of physics. (E.g. MOND was designed to fit rotation curves with the parameter $a_0$, successfully extrapolated to the BTFR, but has limited success with vertical star motion and the dynamics of galaxy clusters.) Other modified gravity approaches, including MOG, conformal gravity, and dozens of others, have not led to a progressive alternative either.

    Perhaps it would be more productive to step away from gravity, and instead examine carefully other physical mechanism produced by known physics. The close relationship between baryonic matter and the importance of gases in galaxy dynamics is particularly intriguing. Why do *ionized*-gas-rich galaxies often exhibit pronounced mass discrepancies? Galaxy clusters also contain substantial quantities of hot, *ionized* gas.

  16. Hi Stacy.

    Thank you (and Prof Jim Schombert) for this post on “CDM, what would Popper do?”

    In everyday life we are used to things being either True or False. In science this seems to apply to observations as well. So, was the wobble in the orbit of Uranus True or False? Repeated observations showed that the wobble was a real effect and so this was True. In particle physics there are numerous occasions where new particles are apparently detected, only for additional observations to show that the anomalies go away – there was no new particle and the observation was shown to be False. (Personally, I think this will happen with the single LZ event as well.)

    The question of True or False seems to fail when applied to the explanations, i.e. to the theories and hypotheses. As Jim Schombert points out, you cannot prove a theory True, but you can Falsify it. The problem seems to be that many theories have an infinite amount of wriggle room (e.g. Dark Matter) and seem to be able to wriggle their way out of all & every apparent Falsification. I suggest that we need to replace “True or False” with “Undecided or False”. So, for “Does Cold Dark Matter (CDM) exist?”: it can’t be Falsified and it can’t be proved True, but it can be Undecided. And apparently, every attempt to disprove General Relativity has failed, so it too is neither False nor True, and I would label it as Undecided.

    You mention explanatory power (I agree with this). So perhaps we should be asking the Yes/No question of whether or not a theory provides a good explanation of an observation. Does Newtonian Gravity provide a good explanation of Uranus’ orbit? Answer: “Yes”, when you add in the planet Neptune.
    Consider galaxy rotation curves.
    (a) Do disk galaxies show flat rotation curves? This is an observation and has the answer: True.
    (b) Is CDM the correct theory? Answer: Undecided (neither True nor False)
    (c) Is MOND the correct theory? Answer: Undecided (neither True nor False)
    (d) Does CDM provide a good explanation of galaxy rotation curves? Answer: Yes.
    (e) Does MOND provide a good explanation of galaxy rotation curves? Answer: Yes.
    This leaves us in the awkward situation of having two distinct explanations for the same phenomenon.

    Back to the original question: “CDM, what would Popper do?” Popper would say that CDM has not been falsified and we should keep on making fresh observations and coming up with new tests.

    1. You say ‘The question of True or False seems to fail when applied to the explanations, i.e. to the theories and hypotheses’. I disagree – on the conceptual side of physics, which is often overlooked and much needed now, there’s a kind of truth that’s very important. When they were trying to understand heat, there were different explanations – a liquid that pours from one object to another when heat is transferred, and so on. And there was a ‘true’ explanation: increased particle motion within an object makes it hot, and heat is an emergent phenomenon. That answer was true, the other answers were false.

      Although we may never have a 100% complete description – we just go nearer and nearer it – we know what’s happening with heat easily well enough to make progress on that basis, which is why the conceptual side is so valuable. That insight eventually led to equations for the motion of particles.

      You say ‘Does Newtonian Gravity provide a good explanation of Uranus’ orbit? Answer: “Yes”, when you add in the planet Neptune’. To me this is way wrong, that’s not an explanation, that’s just mathematical theory and better data.

      In areas where we don’t yet know what’s going on, some people try to wriggle out of admitting there’s truth out there that we don’t know about yet. In the 20th century we were conditioned to think we (sort of) knew it all. But John Wheeler said in an interview ‘it’s not just a matter of nice simple formulas, there’s some ideas out there waiting to be discovered’.

      So even if we’re undecided about what’s underneath the mass discrepancy, nature isn’t. It may not be one of our present explanations, but there’ll be one. Like with heat, and many other breakthroughs in understanding, there’s always a conceptual basis underneath what we observe. And if you admit it’s there, and what we don’t know, as all the great physicists have, the chances of finding it go way, way up.

      1. Also, calling GR undecided is not unreasonable, but it’s not quite true that every attempt to disprove it has failed. That’s a bit like saying every attempt to disprove LCDM has failed – in the current climate a lot of points will be ignored. GR has had failures that would be considered easily enough to falsify a smaller theory, and the evidence against it has been building up steadily. But as they say, it has passed every test ((that people tend to talk about)) with flying colours.

        The echoes in the LIGO gravitational wave signal from a BH merger looked much more certain after a paper from a Perimeter Institute team, Afshordi et al. argued that the chance of the signal being background noise was about 1%.

        The vacuum energy was predicted by reliable QFT, then measured via the Casimir effect, which confirmed the prediction (scientific method in action). According to GR that energy should create lot of gravity, but it doesn’t, and the solar system would fall apart if it did. This point actually weakens the idea that we can assume DM causes the extra gravity in the mass discrepancy.

        Then nearer to home, you have all the evidence for the external field effect, a lot of which came from Stacy. That doesn’t just go against LCDM, it goes against GR as well.

        Apart from experimental results, it doesn’t fit with QM, and no-one thinks QM is to blame. QM connects well with other physics in many places, unlike GR. Recently people have started to say out loud what many have thought for longer, including Sabine Hossenfelder and Raphael Bousso, that GR is a large-scale approximation – and that means wrong.

    2. I disagree with (d): CDM does NOT provide a good explanation of galaxy rotation curves. It predicts cusps where DM halos with cores are preferred (https://tritonstation.com/2017/07/07/aint-no-cusps-here/); it predicts declining rotation curves where they are observed to remain flat (https://tritonstation.com/2024/06/18/rotation-curves-still-flat-after-a-million-light-years/), and it doesn’t get the connection between small and large radii right either (https://iopscience.iop.org/article/10.1086/511807). So if you don’t mind it missing its predicted mark at small, intermediate, and large radii, it does great as an “explanation.” Even then, what it absolutely does not explain is the direct connection between the baryon distribution and the observed kinematics.

  17. “The Rotation Curve of the Milky Way: State of the Art, the Keplerian Decline Debate, and Implications for Dark Matter” by Alessandro Melchiorre & Ruchika, September 2026
    https://arxiv.org/abs/2608.10189
    seems to lack emphasis on the importance of FUNDAMOND (whatever that might be). We know that MOND is falsified whenever special relativity is essential for understanding the data. If general relativistic gravitational lensing is replaced in terms of FUNDAMOND + GR gravitational lensing, then the whole Milky Way rotation curve debate might be radically altered.

  18. It’s good to have an update on MOND now and then; I’m specifically waiting for more stringent requirements from the wide binary analysis. It’s in a way even good that there also is a group trying to disprove the EFE there, that gives motivation to really present what the data tells, clearly and unrevocably. I don’t believe the latest Banik-group claims anymore, and the data is messy, leading to greater freedom to explain whatever if you do not impose stringent quality cuts like Chae and Hernandez. On the side of predicting the data, MOND has always excelled. My own best bet for the theoretical side of MOND didn’t work out unfortunately, so I’ll just try to follow what Milgrom thinks in the theoretical direction.

Comments are closed.